Weak-value Metrology and Shot-Noise Limited Measurements

This thesis contains a subset of the research in which I have participated in during my studies at the University of Rochester. It contains three projects and one overarching theme of weak-value metrology.;We start with chapter 1 where we cover the historical background leading up to quantum optics, which we use for precision metrology. We also introduce the weak-value formulation and give examples of metrological implementations for parameter estimation.;Chapter 2 introduces two experiments to measure a longitudinal velocity and a transverse momentum kick. We show that weak-value based techniques are shot-noise limited because we saturate the Cramer-Rao bound for the estimator used, and efficient because we experimentally demonstrate there is virtually no loss of Fisher information of the parameter of interest from the discarded events.;In Chapter 3 we present a comparison of two experiments that measure a beam deflection. One experiment is a weak-value based technique, while the other is the standard focusing technique. We set up the two experiments in the presence of simulated technical noise sources and show how the weak-value based technique out performs the standard technique in both visibility and in deviation of the transverse momentum kick. Chapter 4 contains work of the exploration of concatenated postselection for weak-value amplification. We demonstrate an optimization and conditions where postselecting on two degrees of freedom can be beneficial to enhance the weak-value amplification.